Light guide fibers having diametrically variable indices of refraction are known. Such fibers have a parabolic curve associated with their indices of refraction. Thus, in the middle of such a light-guide fiber, the refractive index is highest while at the circumferential edge of such a light-guide fiber the refractive index has its lowest value. The production of this type of light-guide fiber has been accomplished previously either by precipitation from a gas phase, such as is described, for example, in the publication by R. D. Maurer, 10th Int. Congr. on Glass, Kyoto, Japan (1974) pp. 59-63, or by an ion exchange process, such as is described, for example, in the publication by J. Kitano, K. Koizumi, H. Matsumura, T. Uchida, M. Furnkawa, Proc. Int. Conf. Solid State Devices, Tokyo, (1969), pp. 63-70.